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Ramsey numbers of generalized fans versus multiple cliques

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  • Wang, Ze
  • Zhang, Yanbo

Abstract

Let r(G, H) denote the Ramsey number for two graphs G and H. The notation nH represents the union of n disjoint copies of H, and K1+nH denotes the graph obtained by joining a new vertex to every vertex in nH. Let h=|V(H)| and ℓ=r(Kp,H). Hamm, Hazelton, and Thompson (Discrete Appl. Math., 2021) proved that for sufficiently large nh, r(tKp,K1+nH)=nh(p−1)+t. Subsequently, Chung and Lin (Adv. Appl. Math., 2025) observed that the proof requires further justification. In this paper, we prove that if n≥max{6(p−1)(ℓ+t)/h,(p−1)(t−1)}, thenr(tKp,K1+nH)=nh(p−1)+t.Our proof combines the theorem by Andrásfai, Erdős, and Sós (Discrete Math., 1974) with a result by Haxell (Combin. Probab. Comput., 2001) on independent transversals.

Suggested Citation

  • Wang, Ze & Zhang, Yanbo, 2026. "Ramsey numbers of generalized fans versus multiple cliques," Applied Mathematics and Computation, Elsevier, vol. 522(C).
    • Handle: RePEc:eee:apmaco:v:522:y:2026:i:c:s0096300326000378
    DOI: 10.1016/j.amc.2026.129985
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